Hi Wendy,
First criteria is the priority of the incident, this will not answer your question all by itself as it needs to be combined with something more tangible. This will be the maturity of your Service Desk manager or team leader.
I used to work in the support department quite some time ago and it was the responsibility of the team leader to decide on the time to functionally escalate the incident based on various the factor (the customer, the general relationship with this customer, the current relationship with the customer - in case they are frustrated by some other issue, the availability of resources, ...)

The answer to this is simple... It's not your call. It's a decision for the Product and Service "Owners" to make.

Every Product and/or Service you support at the front line is managed by a Product Owner or Service Owner that is fully accountable for the products and services they provide. As a responsibility associated with the ownership and accountabiliyt for offering these Products and Services, they work with their customers & end users to set Service Level Expectations/Agreements.

What you call the Front Line is what is commonly referred to as Level 1 Incident Management, which is put in place to keep the Product and Service experts from being distracted from other more critical work they're doing. The Product and Service experts exist at Levels 3 & 4 of the escalation chain. The front line is in place to facilitate the work of the experts so that they don't get distracted from fixing defects and implementing new requirements. In other words, their job is to move Products and Services forward in their maturity cycle. As a result, they put in a front line to "block" incidents that would distract them from such work.

All of this being said, I recommend you sit with the Product and Service owners to have "them" define how long it is acceptable for you to spend on an Incident before escalating to Level 2 (Service Delivery), to Level 3 (the product & service owners themselves), and to Level 4 (the vendors).

Remember, no one knows the Products and Pervices better than the people that created/engineered them. If you spend too long waiting to engage them, you may unnecessarily impact the end user too much. If you engage them too quickly, you will distract them from other more critical work. The biggest way you can add value to them is to help them understand things like the common complexities and trends associated with the work loads. This will help them make better SLA decisions.

Ultimately, I recommend you simply work with them to find a happy medium. You are their eye and ears with respect to the front line and can provide them with a very valuable perspective and data for them to make the best decisions they possibly can.